blackIn this paper blackwe generalize the univariate regression approach of [1]}. Specifically, by extending the MAL density of [2]} – allowing the blacklocation and scale parameters of the MAL to vary over time – we estimate the pair of VaR and ES associated to each asset using a joint quantile regression framework. blackIn this way, we are able to calculate the time-varying VaR and ES simultaneously for all marginal response variables, accounting for possible correlation among the considered assets.
blackFor the VaR components, we assume a CAViaR specification (see [3]}). Parameter estimation is carried out using a suitable EM algorithm as in [2]}, properly extended to deal with the time-varying setting. blackIn this way, the estimated parameters account for tail interdependence among multiple returns and convey this information onto the VaR and ES estimates.
